Inaugural Article: Ising (conformal) fields and cluster area measures

摘要

We provide a representation for the scaling limit of the d = 2 critical Ising magnetization field as a (conformal) random field by using Schramm–Loewner Evolution clusters and associated renormalized area measures. The renormalized areas are from the scaling limit of the critical Fortuin–Kasteleyn clusters and the random field is a convergent sum of the area measures with random signs. Extensions to off-critical scaling limits, to d = 3, and to Potts models are also considered.